Wall slip and hydrodynamics of two-dimensional journal bearing

In the present paper, based on the limiting shear stress model, a multi-linearity finite element algorithm and quadratic programming technique are used to study the influence of wall slip on the hydrodynamic lubrication performance of a two-dimensional journal bearing (finite length journal bearing). It is found that if the lubricated surfaces are designed as homogeneous slip surfaces, the hydrodynamic force will be decreased. If the shaft surface (rotation) is a slippery surface with very low limiting shear stress, almost no fluid load support can be generated. If the sleeve surface is designed as the homogeneous slip surface, a low fluid load support together with a small friction drag can be obtained. However, if the sleeve surface is designed as an optimized slip surface with a slip zone in the inlet region, a high load support and low friction coefficient can be obtained. Optimization of the shape and the size of the slip zone can give the journal bearing many advanced properties.     

The numerical analysis of the radial sleeve bearing with combined surface slip

In order to improve the carrying capacity and reduce the temperature rise in high speed and precise spindle systems, a combined surface radial sleeve bearing using the interfacial slip technique was discussed. An extended Reynolds equation was derived based on the modified slip length model considering the limiting shear stress. By means of the finite differential methods, the characteristic analysis and optimization of the slip region of the combined surface sleeve bearing were carried out, and it has been proved that there is still a considerable large load support in a parallel sliding gap. Comparing with the general journal bearing, the load capacity and end leakage rate of the combined surface sleeve bearing can be increased greatly and the load capacity can be increased by 1.75 times. The attitude angle, friction drag, temperature rise of the combined bearing can be decreased distinctly and the temperature rise can be decreased by 92.4%.     

Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip

Reynolds lubrication theory assumes that there is no wall slip on the interfaces between the solids and lubricant. During recent years, however, it is found that wall slip often happens. The present paper analyzes the wall slip occurring in a hydrodynamic lubrication journal bearing. If the two surfaces have the same adhesion property wall slip always decreases the oil film load support capacity. If there is wall slip over all of the lubricated surfaces, the hydrodynamic effect of the journal bearing vanishes, and no load support exists. If the two lubricated surfaces have different adhesion properties, the wall slip effect is more complex and may cause the journal bearing to operate in an instable manner. In order to avoid the wall slip, the limiting shear stress at the bearing surface should be higher than that at the journal surface.     

滑动轴承二维流场的滑移现象研究

目前对于二维流场及复杂流场的界面滑移分析很少,根据螺旋油楔滑动轴承能使润滑剂产生周向和轴向二维流动的独特的结构特点,考虑周向和轴向两方向的滑移建立基于极限切应力的数学模型,并通过试验和理论对比验证模型的正确性。试验方面运用"目标速度跟踪法"证实了周向和轴向都存在滑移,获知随着供油压力的提高滑移速度有所提高,并且提出轴瓦和轴表面的极限切应力;理论方面运用有限差分法和试验测得的轴瓦和轴表面极限切应力,求解四种状态的广义雷诺方程,发现滑移发生在极限切应力大、间隙小和油膜的封油面区域;考虑界面滑移时,螺旋油楔滑动轴承的承载力和摩擦阻力有所降低;偏心率、螺旋角和转速的变化,影响着承载力和摩擦阻力降低的幅度。     

Theoretical Prediction of Journal Bearing Stability Characteristics Based on the Extent of the Slip Region on the Bearing Surface

Journal bearing performance depends on the boundary conditions at the interfaces between the fluid and the solid surfaces. In the derivation of the Reynolds equation used to predict the bearing performance, the no-slip boundary conditions of the fluid and the solid interfaces are used. Recent research has shown that a slip can occur on specially made surfaces, the conventional no-slip boundary conditions are not valid, and the Reynolds equation is no longer applicable. If the slip is allowed to occur in certain regions, the fluid flow in the bearing can be altered, and the bearing stability characteristics can be improved. In this article, the numerical stability analysis of a journal bearing based on the extent of the slip region on the bearing surface is analyzed. An extended Reynolds equation is derived based on the slip length model, using a no-slip boundary condition against the journal surface and the slip against the bearing surface. A linearized perturbation method is used to determine the stability limit of a rigid rotor supported on two symmetrical journal bearings. Using the linear stability analysis, the linearized stiffness and damping coefficients, the threshold speed, and the critical whirl ratio are evaluated. The effects of the slip parameter on the bearing stability performance are discussed. The results show that with a critical shear stress of zero, an increase in the stability threshold can be achieved with a higher value of the nondimensional slip length and a smaller extent of the slip region on the bearing surface.     

Numerical analysis of spiral oil wedge sleeve bearing including cavitation and wall slip effects

The modified Reynolds equation is established on the basis of critical shear stress model, in which the circumferential and axial wall slip of sleeve and journal surface is considered. Cavitation is treated using modified Elrod algorithm that simplifies the solution of modified Reynolds equation in the full‐film region. The modified Reynolds equations considering wall slip and cavitation effect for two‐dimensional sleeve bearing are established. The results show that wall slip decreases oil film pressure, carrying capacity, friction drag and temperature rise but increases end leakage and cavitation region. The obtained results using the mass‐conserving boundary condition are compared with the Reynolds boundary condition. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical Analysis of a Slider Bearing with a Heterogeneous Slip/No-Slip Surface

The behavior of a fluid-film bearing depends on the boundary conditions at the interfaces between the liquid and the solid bearing surfaces. For almost all solid surfaces, the no-slip boundary condition applies. However, a number of researchers have recently found that slip can occur with specially engineered surfaces. These include molecularly smooth surfaces and surfaces with micron-scale patterns. By constructing an engineered heterogeneous surface on which slip occurs in certain regions and is absent in others, the flow in the liquid film of a bearing can be altered, and such characteristics as load support and friction can be improved. In the present study, a numerical analysis of a slider bearing with such an engineered slip/no-slip surface is analyzed. Slip is assumed to occur when a critical shear stress is exceeded and follows the Navier relation. The results show that with a critical shear stress of zero, a significant increase in load support and decrease in friction can be achieved with an appropriate surface pattern. With nonzero values of critical shear stress, an instability occurs over a range of speeds. At speeds above this range, the bearing behaves similar to the case with zero critical shear stress, while below this range it behaves like a conventional bearing.     

Boundary slip surface design for high speed water lubricated journal bearings

This paper presents the development of a numerical model for high speed and water lubricated journal bearings with different boundary slip arrangements. The effect of boundary slip and its possible mechanism are analyzed and discussed. The results suggest that a suitable combination of slip/no-slip surfaces on the sleeve of a journal bearing enables improvement of the tribological performance through (i) suppressing the occurrence of cavitation, (ii) enhancing the load bearing capacity, and (iii) reducing the interfacial friction between bearing sleeve and shaft. Such improvement becomes more significant for the bearings with smaller eccentricity ratio, smaller width and larger diameter.     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.     

Evidence of lubricant slip on steel surface in EHL contact

The limiting traction provided by typical elastohydrodynamically lubricated (EHL) contacts leads to the postulation that liquid lubricants are subject to limiting shear stress, which is generally accepted as an intrinsic property of the lubricants. The results of recent optical EHL research show that lubricant at EHL contacts may slip on the Cr-coated glass surface under certain circumstances. This paper presents further evidence that high pressure EHL film can slip on a steel surface. Because the steel/steel contacts are common in typical traction drives and the interfaces are therefore oil/steel, the deduction of the limiting shear stress of lubricants from the measured limiting traction may simply reflect a property of the system should boundary slippage occur.     

The influence of sleeve surface roughness on the load-carrying capacity of journal bearings in a magnetic field

The influence of bearing sleeve roughness on the pressure distribution, temperature distribution and load-carrying capacity of a journal bearing in a magnetic field is discussed.The magnetic field increases the load-carrying capacity of the bearing with a smooth sleeve to a greater extent than it increases that of the bearing with a rough sleeve.     

边界滑移对柱塞偶件间油膜流动规律的影响

斜盘式轴向柱塞泵内柱塞偶件间油膜为相对运动的偶件提供润滑及密封作用。油膜流动将直接影响柱塞偶件的工作性能。深入分析偶件间油膜的流动规律对设计与优化柱塞偶件有重要意义。基于Navier-Stokes（N-S）方程,引入Navier边界滑移推导偶件间油膜流动方程,根据柱塞运动的周期性规律,分析单个周期内滑移长度和柱塞泵转速对油膜流动剪应力及流量的影响。研究发现：吸油阶段时近柱塞壁面处油膜剪应力随滑移长度增大而减小,流量随着滑移长度增大而增大,柱塞运动速度最大且滑移长度由1 μm增大到3 μm后,剪应力减小18%,流量增大13.59%;排油阶段柱塞运动速度越大,近柱塞壁面处剪应力和油膜流量与无滑移条件下的差距越小。在滑移长度为1 μm的条件下柱塞泵转速由1 500 r/min增大到4 000 r/min时,近柱塞壁面处的油膜剪应力与无滑移条件下相比降低明显,一个周期内油膜总流量与无滑移条件下相比差距减小。     

The Stability Margin of a Roughened Hole-Entry Hybrid Journal Bearing System

The present work describes a theoretical investigation into the effect of surface roughness on the stability margin of an orifice-compensated, hole-entry hybrid journal bearing system. A modified form of the average Reynolds equation is used for the solution of a lubricant flow field in the clearance space of a rough journal bearing system. The effects of surface roughness parameter (Λ), variance ratio (V?_rj), and the surface orientations (γ) on the bearing flow, load-carrying capacity, and stability threshold speed margin are studied. The study indicates that the bearing configurations having surface roughness on one of the opposing surfaces (stationary or moving roughness) show an opposite trend between stability threshold speed margin and load-carrying capacity. However, the bearing configurations having transverse- and isotropic-type roughness patterns on both bearing and journal surfaces provide an improved value of both stability threshold speed margin and load-carrying capacity only when the surface roughness has a variance ratio value between 0.49 and 0.59 for the transverse roughness pattern and between 0.59 and 0.84 for the isotropic roughness pattern.     

Numerical investigation of pocketed slip slider bearing with non-Newtonian lubricant

Boundary slip as well as surface texturing is an effective method to improve the tribological performance of lubricated mechanical components. This article analyzes the combined effect of single texturing (pocketing) and wall slip on pressure that strongly related to the load-carrying capacity of slider bearing. The modified Reynolds equation for lubrication with non-Newtonian power-law fluid is proposed. The equation was solved numerically using a finite difference equation obtained by means of the micro-control volume approach. Further, numerical computations for slider bearing with several power-law indexes were compared with the presence of the pocket and slip. The numerical results showed that the characteristic of non-Newtonian is similar to Newtonian fluid with respect to hydrodynamic pressure distribution. The maximum load support is achieved when the pocket depth is equal to the film thickness.     

柔性支承结构对可倾瓦轴承稳定性的影响

为了进一步提高可倾瓦轴承支承转子系统的稳定性，提出由弹簧支承的柔性可倾瓦轴承结构。设计制造单层弹簧和双层弹簧支承的2种柔性可倾瓦轴承试样，在转子-轴承实验台上开展稳定性实验研究。实验结果表明：由弹簧支承的柔性可倾瓦轴承综合支承刚度小于普通可倾瓦轴承的支承刚度，新型柔性可倾瓦轴承具有降低转子临界转速的作用；相比于普通可倾瓦轴承，柔性支承可倾瓦轴承明显降低轴频振幅，能够有效提高转子-轴承系统的运行稳定性，且双层弹簧支承的可倾瓦轴承稳定性提高更为显著。     

基于ANSYS的轴承保护环的设计

矿山机械中转子-轴承系统采用传统的设计方法很容易发生故障,基于一种新的设计方法,给转子-轴承系统增加了一个轴承保护环,并通过ANSYS有限元分析软件对其形状进行了优化,最后在试验室柔性转子动平衡系统上进行弹性振动试验可知,转轴运动轨迹中的高次谐波信号得到了很好的抑制,轴承保护环使得轴承基本上不与系统发生共振,大大增加了轴承的使用寿命.     

涡轮泵流体静压轴承设计及性能特性分析

针对流体静压轴承在液体火箭发动机涡轮泵中的设计和应用,以现有的滚动轴承支承的涡轮泵转子为应用对象,提出流体静压轴承的参数设计思路,采用粒子群优化算法设计得到支承刚度最大化的轴承结构参数组合,并计算分析所设计轴承的性能以及轴承-转子系统的动力学特性。分析表明：优化设计得到流体静压轴承的承载力和支承刚度可以满足要求,但轴承总流量达泵流量的21%,这会显著降低涡轮泵的总体效率;仅将滚动轴承改为流体静压轴承,而不改变其他结构或布局,转子的稳定性不能满足要求;涡轮泵流体静压轴承转子系统设计时应尽量将轴承布置在转子位移较大的位置,以充分发挥其阻尼作用。     

Design of Slip Boundary Produced by a Lotus Structure Applied to a Hydrostatic Bearing

Hydrostatic bearings (HSBs) are widely used in large-size precision machines because of the features of high load-carrying capacity, high stiffness, and high accuracy. This study focuses on enhancing the performance of HSBs by modifying the boundary condition from non-slip to slip. The lotus structure underneath the bearing land was designed to achieve this modification based on the developed theoretical model and simulation results. Three major theoretical works were conducted: (1) modification from the non-slip boundary condition to a slip condition; (2) establishment of the relationship between the slip length and the height of the lotus structure with various area fractions of oil–air interface; and (3) design of the lotus structure to create the required slip length. Finally, the microchannel and the biomimetic lotus structure were fabricated for the purpose of simulating the slip boundary condition on the surface of the bearing land. Superior bearing performances and reduced energy consumption were obtained by increasing the slip length.     

Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery

The fluid dynamics of gas-lubricated journal bearings in micro-rotating machinery is different from those of larger size. One point to be considered is a slip flow effect. In this paper, the slip flow effect is considered in order to estimate load-carrying capacity and dynamic coefficients of micro gas-lubricated journal bearings. Based on a modified compressible Reynolds equation including slip flow effect, the first slip approximation was applied. To extract dynamic coefficients, the linearized dynamic equations were formulated by the perturbation method. Numerical predictions compared the static and dynamic characteristics considering slip flow at room-to-high temperature in a range of bearing numbers. The results including load-carrying capacity and dynamic coefficients demonstrate that the slip flow effect becomes significant with temperature increase as well as in the lower range of bearing numbers.     

Conical whirl instability of turbulent flow hybrid porous journal bearings

An analysis of conical whirl instability of an unloaded rigid rotor supported in a turbulent flow hybrid porous journal bearing has been presented, following Constantinescu's turbulent lubrication theory. The effect of bearing feeding parameter (β), Reynolds number (Re), ratio of wall thickness to journal radius (H/R) and anisotropy of porous material on the stability of rotor-bearing system has been investigated. It is observed that higher values of β gives better stability and higher stability is predicted if the porous bush is considered to be isotropic.